Weighted Hardy spaces on an interval and Poisson integrals associated with ultraspherical series

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Boundedness of Singular Integrals in Weighted Anisotropic Product Hardy Spaces

Let Ai for i = 1, 2 be an expansive dilation, respectively, on R n and R and ~ A ≡ (A1, A2). Denote by A∞(R × R; ~ A) the class of Muckenhoupt weights associated with ~ A. The authors introduce a class of anisotropic singular integrals on R×R, whose kernels are adapted to ~ A in the sense of Bownik and have vanishing moments defined via bump functions in the sense of Stein. Then the authors est...

Extension of Hardy Inequality on Weighted Sequence Spaces

Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...

Bounds of Singular Integrals on Weighted Hardy Spaces and Discrete Littlewood–Paley Analysis

We apply the discrete version of Calderón’s reproducing formula and Littlewood–Paley theory with weights to establish the H w → H w (0 < p < ∞) and H w → Lw (0 < p ≤ 1) boundedness for singular integral operators and derive some explicit bounds for the operator norms of singular integrals acting on these weighted Hardy spaces when we only assume w ∈ A∞. The bounds will be expressed in terms of ...

Generalized composition operators on weighted Hardy spaces